Translations
Translate point A(3, 6) 3 units up and one to the left
A'(2, 9)
Reflect the point A(3, 9) over the y-axis
Rotate the point A(3, 1) 90o clockwise around the origin
A'(1, -3)
Dilate the point A(2, 9) by a scale factor of 2
A'(4, 18)
Reflect the point A(6, 1) over the y-axis and then dilate it by a scale factor of 3
A''(-18, 3)
Translate the triangle A(1, 2), B(4, 2), and C(3, 5) by 2 units to the left and three units up
A'(-1, 5), B'(2, 5), C'(1, 8)
Given the point P(−3,5), reflect it across the x-axis.
P'(-3,-5)
Given the point P(3,2), rotate it 90 degrees clockwise about the origin.
P'(2, -3)
Given the point Q(−6,8), apply a dilation about the origin with a scale factor of 1/2.
Q'(-3, 4)
Point P(2,−3) is first translated 4 units to the right and 2 units up, then reflected across the x-axis.
P''(6, 1)
Consider a quadrilateral with vertices at D(2,8), E(5,8), F(5,4), and G(2,4). Translate the quadrilateral by moving every point 3 units to the left and 4 units downward.
Question: List the coordinates of the new vertices after the translation.
D'(-1, 4), E'(2, 4), F'(2, 0), G'(-1, 0)
A triangle has vertices at A(1,−2), B(3,4), and C(5,0). Reflect the entire triangle across the y-axis.
A'(-1, -2), B'(-3, 4), C'(-5, 0)
A triangle has vertices at A(1,2), B(3,5), and C(4,1). Rotate the triangle 180 degrees about the origin.
A'(-1, -2), B'(-3,-5), C'(-4,-1)
A triangle has vertices at A(2,1), B(4,3), and C(3,−1). Dilate the triangle about the origin using a scale factor of 3.
A'(6, 3), B'(12, 9), C'(9, -3)
Triangle ABC has vertices A(1,2), B(3,2), and C(2,4).
First, the triangle is dilated about the origin by a scale factor of 2.
Then, the image is translated 1 unit left and 3 units down.
Question: What are the final coordinates of triangle A′B′C′?
A''(1,1), B''(5,1), C''(3, 5)
A point Q(−3, 4) undergoes two successive translations. First, it is moved 6 units to the right and 2 units downward. Then, it is moved 1 unit to the left and 7 units upward.
Question: Find the coordinates of Q after both translations. Also, determine the single translation (in terms of units to the right/left and upward/downward) that is equivalent to these two successive moves.
A''(2, 9)
5 units to the right and 5 upwards
Reflect a quadrilateral with vertices at D(1,2), E(2,5), F(4,5), and G(5,2) across the x-axis
D'(1, -2), E'(2, -5), F'(4, -5), G'(5, -2)
A quadrilateral has vertices at D(1,1), E(4,1), F(4,3), and G(1,3). Rotate the figure -90 degrees clockwise about the origin.
D'(-1, 1), E'(-1, 4), F'(-3, 4), G'(-3,1)
The image of a point after a dilation about the origin with a scale factor of 4 is (12,−8).
Question: What were the coordinates of the original point before the dilation?
(3, -2)
Quadrilateral WXYZ has vertices at W(1,0), X(2,2), Y(4,2), and Z(3,0).
First, rotate the figure 180 degrees about the origin.
Then, translate the figure 3 units right and 1 unit up.
Question: What are the coordinates of the new vertices?
W''(2, 1), X''(1,-1), Y''(-1,-1), Z''(0,1)
Two shapes in the coordinate plane are given.
Shape 1: Vertices at (2,3), (2,7), and (5,5).
Shape 2: Vertices at (7,−1), (7,3), and (10,1).
Question: Can a translation map Shape 1 to Shape 2? If so, specify the translation by stating how many units the shape is moved to the right or left and upward or downward.
yes, translated by 5 units to the right and 4 down
A triangle has vertices at A(2,−1), B(4,3), and C(0,2). Reflect the triangle across the x-axis.
A'(2, 1), B'(4, -3), C'(0, -2)
A triangle has vertices at A(−2,3), B(0,5), and C(1,1). Rotate the triangle 90 degrees clockwise about the origin.
A'(3, 2), B'(5, 0), C(1, -1),
Given the point R(5,−2), apply a dilation about the origin with a scale factor of –2.
R'(-10, 4)
The point P(3, 6) is rotated 180 degrees about the origin and then dilated by a scale factor of 1/3.
describe a single transformation that is the same as the compound transformation described above and give the new coordinates of the point
Dilation by scale factor of -1/3
P'(-1, -2)